Entanglement [1]} is one of the most distinctive features of quantum mechanics which manifests as nonlocal correlations [2]} in quantum systems [3]}, [4]}. The maximally entangled Bell states [5]} have played a significant role in illustrating the nature of quantum correlations, as well as their usefulness in quantum tasks [6]}. They have found applications in quantum cryptography [7]}, quantum teleportation [8]},
super dense coding [9]}, to mention a few well known examples. The three particle Greenberger–Horne–Zeilinger (GHZ) state [10]}, its generalisations and W-states are known to show stronger non-locality and different entanglement properties [11]}, [12]}. These states have found use in quantum information splitting [13]}, [14]}, [15]}, quantum teleportation [11]}, [17]}, [18]}, [19]} and revealed subtle phase structure in atomic systems [4]}, [21]}. It has been shown that a pure EPR pair [17]} and a more general form of two qubit [18]} can be teleported deterministically and faithfully, using GHZ like states as a channel and performing projective measurements over the GHZ like basis states. In contrast, a GHZ state and an SLOCC equivalent W-class state [11]} can only teleport an arbitrary single qubit state. Moreover, quantum secret sharing via the GHZ like states has been shown to be more efficient as compared to GHZ states [14]}. From the application perspective, the GHZ like states are more robust and efficient as compared to GHZ and W-class of states.
Significantly, the implementation of quantum tasks has revealed the physical nature of the quantum non-local correlations [26]}. The non maximally entangled states fail to teleport deterministically [27]} and the three qubit states get divided into two distinct classes [28]}; the GHZ class shows deterministic teleportation and W class fails to do so [29]}.
The entangled states of higher dimensions are under intense investigation [30]} as they provide advantage over qubit states and show better quantum correlations by strongly violating the Bell's inequality. Entanglement has also thrown considerable light on correlations in spin chains [31]}, [32]} and quantum many body systems [33]}.
Therefore, understanding of the physical nature of entanglement has attracted considerable attention in the current literature [26]}, [35]}, [30]}.
